Angular Distribution of Charge-Exchange Scattering of 40-Mevπ−Mesons by Hydrogen

Abstract

The angular distribution of the reaction ${\pi }^{-}+p\to {\pi }^0+n$ has been measured at a mean ${\pi }^{-}$ energy of 40 Mev by detecting coincident photons corresponding to ${\pi }^0$ emission at approximately 0°, 90°, and 180°. The result is $\frac{d{\sigma }^0}{d\Omega }=(0.45\mathrm{}\pm 0.07)-(0.98\pm 0.13)cos\theta +(0.54\mathrm{}\pm 0.21){cos}^2\theta \mathrm{mb}/\mathrm{sterad}.$ The corresponding total cross section is ${{\sigma }_t}^0=7.9\mathrm{}\pm 1.8$ mb. An analysis of this result and of previous measurements on ${\pi }^{+}$ and ${\pi }^{-}$ scattering at 37 Mev has been made, following the hypothesis of charge independence. It is possible to find two distinct types of solution. One type has positive $T=\frac{1}{2}$ $s$-wave and $T=\frac{3}{2}$ $p$-wave phase shifts, and negative $T=\frac{3}{2}$ $s$-wave and $T=\frac{1}{2}$ $p$-wave phase shifts. For the other type, the signs of the phase shifts are almost all reversed. Each type consists of a pair of solutions which are intrinsically indistinguishable at low energies because of the impossibility of determining the sign of the spin-flip scattering amplitude. A choice between the two types of solution is in principle possible with improved data. Predictions of the angular distributions of ${\pi }^{-}$ elastic scattering are made.